This study focuses on defining the typology of speech acts that follow agreement acts, based on the theoretical assumptions that there are certain identifiable paterns that constitute coherents flows of conversations and that such flows comprise chaining of conversational acts. Special attention has been given to identifving the defining characteristics between the task oriented discourse such as discssions, and the relation-oriented discourse such as chatting. In so doing, the DAMSL system, designed for crosslinguistic standardization of dialog act markup in several layers, was utilized. Despite the differences of conversation types, an investigation of frames of speech act chains across subtypes of agreement acts reveals a striking similariy across such sub-types. In other words, when perlocution is chained with Agreement acts, the [Accept-Accept] chain is formed; when it is chained with Understanding acts, the [Accept-Acknowledge] chain is formed; and further, when it is chained with Response acts, the chain types diverge, i.e., the [Accept-Non-reaction] chain in case of task-oriented conversations, and the [Accept-Back channel] chain in case of relationship-oriented conversations. An exploration into the tendencies associated with the flows of conversations, based on the frequency of speech act chains, has significance in the facts that it enables the construction of the prototypical conversational models among human individuals, and further that its research results can be applicable to developing automated conversation systems of human-machine communication, Remaining issues that are hoped to be addressed in the future research include confirming the research results in larger corpora, and extending them to other speech acts of retrospection functions, which should contribute to the better understanding of the nature of the conversational structures in a broader scale.